Systems and methods for increasing efficiency of ultrasound waveform tomography

ABSTRACT

Ultrasound tomography imaging methods for imaging a tissue medium with one or more ultrasound transducer arrays comprising a plurality of transducers, wherein said transducers comprise source transducers, receiving transducers. The methods include assigning a phase value or time delay to source transducers, exciting the transducers and calculating a search direction based on data relating to the excited transducers.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/339,770, filed on Jul. 24, 2014, now U.S. Pat. No. 10,034,656, issuedon Jul. 31, 2018, which is a 35 U.S.C. § 111(a) continuation of PCTinternational application number PCT/US2013/024676 filed on Feb. 4,2013, incorporated herein by reference in its entirety, which claimspriority to, and the benefit of, U.S. provisional patent applicationSer. No. 61/594,865, filed on Feb. 3, 2012, incorporated herein byreference in its entirety. Priority is claimed to each of the foregoingapplications.

The above-referenced PCT international application was published as PCTInternational Publication No. WO 2013/116866 on Aug. 8, 2013,incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Grant No.MIPR0LDATM0144 from the Breast Cancer Research Program ofDoD-Congressionally Directed Medical Research Programs and Contract No.DE-AC52-06NA25396 awarded by the Department of Energy. The Governmenthas certain rights in the invention.

INCORPORATION-BY-REFERENCE OF COMPUTER PROGRAM APPENDIX

Not Applicable

NOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION

A portion of the material in this patent document is subject tocopyright protection under the copyright laws of the United States andof other countries. The owner of the copyright rights has no objectionto the facsimile reproduction by anyone of the patent document or thepatent disclosure, as it appears in the United States Patent andTrademark Office publicly available file or records, but otherwisereserves all copyright rights whatsoever. The copyright owner does nothereby waive any of its rights to have this patent document maintainedin secrecy, including without limitation its rights pursuant to 37C.F.R. § 1.14.

BACKGROUND OF THE INVENTION 1. Field of the Invention

This invention pertains generally to imaging, and more particularly toultrasound imaging using a synthetic aperture ultrasound waveformtomography.

2. Description of Related Art

Breast cancer is the second-leading cause of cancer death among Americanwomen. The breast cancer mortality rate in the U.S. has been flat formany decades, and has decreased only about 20% since the 1990s. Earlydetection is the key to reducing breast cancer mortality. There is anurgent need to improve the efficacy of breast cancer screening.Ultrasound tomography is a promising, quantitative imaging modality forearly detection and diagnosis of breast tumors.

Ultrasound waveform tomography is gaining popularity, but iscomputationally expensive, even for today's fastest computers. Thecomputational cost increases linearly with the number of transmittingsources.

Waveform tomography accounts for all the wave propagation effects, andis more powerful than diffraction tomography. It is usually carried outwith a numerical simulator and is capable of properly handling complexwave phenomena. However, ultrasound waveform tomography iscomputationally expensive for data acquired using a synthetic-apertureultrasound tomography system, particularly for three-dimensionalimaging. Ultrasound waveform tomography numerically calculatessound-wave propagation from every ultrasound transducer element. In asynthetic-aperture ultrasound tomography system, hundreds to thousandsof transducer elements emit ultrasound, which requires an enormousamount of computational time and resources for ultrasound waveformtomography

Ultrasound waveform tomography could become a high-resolution imagingapproach for breast cancer detection and diagnosis. The maindisadvantage of ultrasound waveform tomography is too computationallyexpensive to be feasible for clinical applications, particularly forlarge datasets acquired using a synthetic-aperture ultrasound tomographysystem that consists of hundreds to thousands of transducer elements.

BRIEF SUMMARY OF THE INVENTION

An aspect of the present invention is a source encoding method forultrasound waveform tomography to greatly improve the computationalefficiency. This method simultaneously simulates ultrasound wavesemitted from multiple transducer elements during inversion. A randomphase is applied to each source to distinguish the effect of differentsources. The random phase helps eliminate the unwanted crossinterference produced by different sources. The method significantlyreduces the computational time of ultrasound waveform tomography to lessthan one tenth of that for the original ultrasound waveform tomography,and makes it feasible for ultrasound waveform tomography in futureclinical applications.

Another aspect is a source encoding scheme for ultrasound waveformtomography using transmission and reflection data fromsynthetic-aperture ultrasound tomography systems. The methodsimultaneously simulates ultrasound propagation from tens to hundreds oftransducer elements during inversion. The approach employs a randomphase on each transducer element to remove the cross interference.

The system and method of the present invention uses ultrasound dataacquired using a synthetic-aperture ultrasound system. Theinvestigational synthetic-aperture ultrasound tomography system of thepresent invention allows acquisition of each tomographic slice ofpatient ultrasound data in real time. In the system, each element of thetransducer array transmits ultrasound sequentially, and elements in thetransducer array simultaneously record ultrasound signals scattered fromthe tissue after each element is fired. The features of the system andmethod of the present invention provide a real-time synthetic-aperturesystem that can be used for patient data acquisition.

In the synthetic-aperture ultrasound tomography system of the presentinvention, ultrasound from each element of a transducer array or avirtual source of multiple elements propagates to the entire imagingdomain, and all elements in the transducer array receive ultrasoundsignals reflected/scattered from the imaging region and/ortransmitted/scattered through the imaging region. Therefore, theacquired synthetic-aperture ultrasound data contain information ofultrasound reflected/scattered and transmitted from all possibledirections from the imaging domain to the transducer array to generate amore accurate, 3-D, high resolution image, while minimizingcomputational costs of the system.

Further aspects of the invention will be brought out in the followingportions of the specification, wherein the detailed description is forthe purpose of fully disclosing preferred embodiments of the inventionwithout placing limitations thereon.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

The invention will be more fully understood by reference to thefollowing drawings which are for illustrative purposes only:

FIG. 1 is a schematic diagram of a synthetic-aperture ultrasound systemin accordance with the present invention.

FIG. 2 is a schematic diagram of a synthetic-aperture ultrasoundtomography system for scanning breast tissue in accordance with thepresent invention

FIG. 3 is a schematic diagram of the scanner of the ultrasoundtomography system of FIG. 1 interrogating a region of tissue.

FIG. 4 shows flow diagram of a method for sequentially exciting a regionof tissue and acquiring reflection and transmission data in accordancewith the present invention.

FIG. 5 illustrates a schematic view of a two parallel-bar ultrasoundtransducer array scanner.

FIG. 6 illustrates a schematic view of a scanner comprising two parallelplanar arrays.

FIG. 7 shows a schematic view of a cylindrical array scanner having acylindral 2-D array of transducers and a 2-D planner array at the bottomof the cylinder.

FIG. 8 shows a flat transducer configured to generate a collimated beam.

FIG. 9 shows an arcuate transducer configured to generate a divergingbeam.

FIG. 10 shows a schematic view of a torroidal array scanner having a acircular array of transducers.

FIG. 11 shows a schematic view of a synthetic-aperture ultrasound breasttomography scanner that incorporates use of two circular transducerarrays.

FIG. 12 shows a schematic view of a scanner comprising a semicircular orarcuate array having transducers in an opposing or facing orientationwith planar array.

FIG. 13 illustrates a scanner that reduces the 2D arrays in FIG. 12 to1D arrays.

FIG. 14 is a flow diagram of a synthetic aperture ultrasound tomographymethod in accordance with the present invention.

FIG. 15 shows an image of a numerical breast phantom containing twodifferent tumors.

FIG. 16A and FIG. 16B show imaging results (tomographic reconstructionin FIG. 16A, and vertical profile along the center of the tumors in FIG.16B) obtained using only the reflection data.

FIG. 17A and FIG. 17B show imaging results (tomographic reconstructionin FIG. 17A, and vertical profile along the center of the tumors in FIG.17B) obtained using only the transmission data.

FIG. 18A and FIG. 18B show imaging results (tomographic reconstructionin FIG. 18A, and vertical profile along the center of the tumors in FIG.18B) obtained using both transmission and reflection data simultaneouslyin accordance with method of the present invention.

FIG. 19 illustrates a method using both transmission and reflection datafor ultrasound waveform tomography.

FIG. 20 illustrates a flow diagram of a source encoding method forultrasound waveform tomography in accordance with the present invention.

FIG. 21 illustrates a flow diagram of a data blending method forultrasound waveform tomography in accordance with the present invention.

FIG. 22 shows an image of two small tumors in the numerical breastphantom scanned using the synthetic-aperture ultrasound tomographysystem similar to that shown in FIG. 1.

FIG. 23A and FIG. 23B show images of reconstruction results ofultrasound waveform tomography without source encoding obtained after 20inversion iterations. FIG. 23A is a 2D image of the original ultrasoundwaveform tomography. FIG. 23B is a horizontal sound-speed profile of thetomography result at the vertical location of 91 mm.

FIG. 24A through FIG. 24D show images of ultrasound waveform tomographyresults obtained using source encoding after 20 iterations for 4, 8, 12and 24 sources respectively.

FIG. 25A through FIG. 25D show images of horizontal sound-speed profilesof FIG. 24A through FIG. 24D at the vertical location of 91 mm for 4, 8,12 and 24 sources respectively.

FIG. 26A through FIG. 26D show images of horizontal sound-speed profilesof the third-iteration result when using source encoding for 4, 8, 12and 24 sources respectively. The vertical location of the profile is at91 mm.

FIG. 27 shows an image of two small tumors in the numerical breastphantom scanned using the synthetic-aperture ultrasound tomographysystem similar to that shown in FIG. 1.

FIG. 28A and FIG. 28B show images of reconstruction results ofultrasound waveform tomography without data blending obtained after 20inversion iterations. FIG. 28A is a 2D image of the original ultrasoundwaveform tomography. FIG. 28B is a horizontal sound-speed profile of thetomography result at the vertical location of 91 mm.

FIG. 29A through FIG. 29C show images of ultrasound waveform tomographyresults obtained using data blending after 20 iterations for 4, 8, and24 sources respectively. The maximum delay time is one period.

FIG. 30A through FIG. 30C show images of horizontal sound-speed profilesof FIG. 29A through FIG. 29C at the vertical location of 91 mm for 4, 8,and 24 sources respectively.

FIG. 31A through FIG. 31C show images of ultrasound waveform tomographyresults obtained using blended data after 20 iterations for 4, 8, and 24sources respectively. The maximum delay time is one period.

FIG. 32A through FIG. 32C show images of horizontal sound-speed profilesof FIG. 31A through FIG. 31C at the vertical location of 91 mm for 4, 8,and 24 sources respectively.

FIG. 33A through FIG. 33C: show images of ultrasound waveform tomographyresults obtained using blended data after 20 iterations for 4, 8, and 24sources respectively. The maximum delay time is one period.

FIG. 34A through FIG. 34C show images of horizontal sound-speed profilesof FIG. 33A through FIG. 33C at the vertical location of 91 mm for 4, 8,and 24 sources respectively.

DETAILED DESCRIPTION OF THE INVENTION

The description below is directed to synthetic aperture ultrasoundtomography systems for imaging a medium such as patient tissue, alongwith ultrasound waveform tomography methods for acquiring and processingdata acquired from these systems, or other systems that may or may notbe available in the art.

The synthetic-aperture breast ultrasound tomography system of thepresent invention uses synthetic-aperture ultrasound to obtainquantitative values of mechanical properties of breast tissues. In thissystem, each transducer element transmits ultrasound waves sequentially,and when an ultrasound transducer element transmits ultrasound wavespropagating through the breast, all ultrasound transducer elements (atleast within a portion of an array) simultaneously receive ultrasoundreflection/transmission, or forward and backward scattering signals. Theultrasound reflection/transmission signals are used to obtainquantitative values of mechanical properties of tissue features (and inparticular breast tumors), including the sound speed, density, andattenuation.

While the systems and methods described below are particularly directedand illustrated for imaging of breast tissues, it is appreciated thatthe systems and methods may also be employed for waveform tomography onother tissues or scanning mediums.

I. Synthetic Aperture Ultrasound Tomography System

FIG. 1 is a schematic diagram of a synthetic-aperture ultrasound system10 in accordance with the present invention. The system 10 includes ascanner 12 comprising a plurality of individual transducer elements 16disposed within one or more arrays (e.g. the opposing parallel arrays 14a and 14 b shown in FIG. 1). The scanner 12 is coupled to a server orlike computing apparatus 20 (e.g. with a cable 15 or other connectionmeans such as, but not limited to, a wireless connections means) andsynthetic aperture ultrasound data acquisition system 18 that outputs RFdata 28 corresponding to readings acquired by the scanner 12.

The computer 20 comprises a processor 24 configured to operate one ormore application programs 22 located within memory 25, wherein theapplication programs 22 may contain one or more algorithms or methods ofthe present invention for imaging a tissue medium for display via agraphical user interface 23 on monitor 26, or other means. For example,the application programming 22 may comprise the programming configuredfor operating the sequential excitation method 50 shown in FIG. 4 orultrasound waveform tomography imaging method 200 shown in FIG. 14. Thecomputer 20 controls ultrasound tomography data acquisition, and theprocess is completed automatically. The whole-breast scanning time withapproximately 100 slides takes approximately 2 minutes.

FIG. 2 is a schematic view of a breast ultrasound tomography system 11in accordance with the present invention. System 11 includes a table 70having a water tank 76 with an open aperture at the top of the table 70for insertion of the patient's breast tissue (which ideally hangspendant within water tank 76 during imaging). Tank 76 includes one ormore synthetic-aperture ultrasound transducer arrays 74 located withinone or more surfaces of the tank. The transducer array(s) 74 areimmersed within the water tank 76 configured for receiving the patientsbreast 44 through aperture 72, and scanning the breast 44 while thepatient is lying down on the table 70 in the prone position. Asdescribed in further detail below, transducer array(s) 74 may comprise anumber of different configurations, with the water tank housing 76shaped accordingly to house the array(s) 74. The water tank housing 76material preferably comprises a light, non-conductive material thatconforms to the shape of the array(s) 74 (e.g. rectangular for2-parallel bar array scanner 12 of FIG. 1, or cylindrical for thescanners 110, 120 and 130 shown in FIG. 7, FIG. 10 and FIG. 11,respectively).

Positioning of the active areas of all array(s) 74 relative to the watertank housing 76 is preferrably aligned such that the ultrasound energyfor the transducer elements 16 (FIG. 1) is focused onto the same planeperpendicular to the housing (for parallel bar scanner 12 (FIG. 5) orplanar 100 (FIG. 6) arrays). The arrays (e.g. arrays 14 a and 14 b,FIG. 1) are preferrably electrically isolated and grounded.

The system 11 includes a data acquisition system 18 that may be coupledto a computer system or electronics 78 that control scanning. The dataacquisition system 18 may also be coupled to a computer 20 for runningapplication programming 22 (FIG. 1) to perform tomographyreconstructions.

During the ultrasound data acquisition in the synthetic-apertureultrasound tomography system 10, the raw ultrasound data 28(radio-frequency data) may be first stored within computer memory 25(FIG. 1) (which may comprise solid state drives or other storage meansavailable in the art), allowing real-time patient data acquisition forclinical applications.

FIG. 3 is a schematic diagram of the two parallel bar arrays 14 a and 14b of scanner 12 of FIG. 1 shown interrogating a region of tissue 44(e.g. breast tissue for mammography) in accordance with a preferredmethod of the present invention. The ultrasound imaging system 10focuses an array 14 a and 14 b of N transducers 16 acting in atransmit-receive mode. Each element of the array 14 a 14 b is excitedsequentially (e.g. transducer 3 of array 14 a is shown in excitationmode) to generate an ultrasound field or signal 30 through the tissuesurface 40 and into tissue medium 44 having a plurality of pointscatterers 42. The backscattered signals 32 are measured in parallel byall N elements 16. In addition, opposing array 14 b transducers arepositioned facing array 14 a such that one or more elements of the array14 b receive direct transmission signals 30 simultaneously withreception of backscatter or reflection signals 32 being received byarray 14 a.

FIG. 4 shows flow diagram of a method 50 for sequentially exciting aregion of tissue 44 in accordance with the present invention. At step52, a first element (e.g. element 1 or i) of array 14 a 14 b of Nultrasound transducer elements 16 is excited for interrogating aninhomogeneous medium 44. At step 54, the backscattered/reflected signals32 are received/measured by all elements 16 (of at least 14 a), whiletransmission signals 30 are received/measured by one or more elements 16of array 14 b. At step 58, the method evaluates whether all the elements16 in the arrays 14 a and 14 b have been excited (and imaged). If thelast element in the arrays 14 a, 14 b has not been reached, the methodmoves to the next element 16 in the array (14 a or 14 b) at step 60, andrepeats the process sequentially until the N^(th) element is reached. Atthis point, the individual reflection/transmission data are RF data, andthe process 50 transfers the RF data to memory or solid state drives 25at step 64.

In the phased transducer arrays for synthetic-aperture breast ultrasoundtomography, a plurality of transducer elements 16 are fired withdifferent delayed times to simulate ultrasound waves emerging from avirtual point source. The systems and methods of the present inventionpreferrably use the virtual point sources of the synthetic-aperturebreast ultrasound tomography system to improve signal-to-noise ratios ofbreast ultrasound data.

The various scanning arrays invention, described below with reference toFIG. 5 through FIG. 7 and FIG. 10 through FIG. 13, are shown toillustrate that the systems 10, 11 and methods 50, 200 may be achievedin various configurations. Yet, the scanning arrays of FIG. 5 throughFIG. 7 and FIG. 10 through FIG. 13 all share at least one commoncharacteristic in that at a plurality of transducers 16 of an array, orportion of an array, oppose (at a spaced-apart distance across thetarget scanning medium 44) a plurality of transducers 16 of eitheranother portion of the array, or a separate array, so that reflectionand transmission data may be acquired with each successive transducerexcitation. The following are specific examples of arrays that may beused in the systems 10, 11 and methods 50, 200 of the present invention.However, other configurations are contemplated. In each of theseconfigurations, the scanner 74 is shown without table 70 or housing 76for clarity.

A. Dual Parallel-Bar Array Scanner

FIG. 5 illustrates a two parallel-bar ultrasound transducer arrayscanner 12, which is illustrated in reference to implementation withinsystem 10 in FIG. 1, and schematically in operation as asynthetic-aperture scanner in FIG. 3.

As shown in FIG. 5, the two arrays 14 a and 14 b are shown in opposingorientation (e.g. facing each other and matching in location alongx-axis in FIG. 5), and positioned in the x-y plane (preferrably parallelto table 70 in FIG. 2, such that they are spaced-apart across thescanning region 44. Each of the 14 a and 14 b comprises a plurality of Ntransducers 16 (e.g. count of 128) linearly aligned in series (shown inalong the x-axis for reference) as parallel-phased arrays firing towardeach other in operation (see FIG. 3).

A robotic stage 90 is provided so that the arrays can move in unisonvertically along the z-axis to scan the tissue 44. The transducer arrays14 a and 14 b are configured to scan the breast 44 from the chest wallto the nipple region, slice by slice. To image the axillary region(region of breast closest to the armpit of the patient, not shown), thetwo transducer arrays 14 a and 14 b can be steered toward the axillaryregion, with one of the transducer arrays placed near the axillaryregion. The axillary region, or basin, is important to oncologicsurgeons, as it represents the principal lymphatic drainage region ofthe breast. Lymphatic metastasis from a malignant breast lesion willmost often occur in this region.

Arrays 14 a and 14 b may also be translated (either in concert, or withrespect to each other) in the x and y axes to closely conform to varyingpatient anatomy.

Referring to FIG. 8 and FIG. 9, the transducer 16 may either be flat orcircular, and the surface of the transducer element 16 may either beflat, as in transducer 16 a in FIG. 8, or arcuate in shape, as shown intransducer 16 b of FIG. 9. The flat transducer 16 a of FIG. 8 generatesa collimated beam 17, whereas the curvilinear transducer 16 b of FIG. 9has a focal point P that is behid the emitting surface to generate adiverging beam 19 (defocused or lens configuration preferably in the y-zplane) across a field of view from A to B (centered on C). Thecurvilinear transducer 16 b of FIG. 9 helps get a 3-D volume whilescanning, and is particularly useful with line arrays such as those inFIG. 5, FIG. 10, FIG. 11, and FIG. 13.

In one embodiment, exemplary dimensions for the arrays 14 a and 14 b andtransducers 16 are as follows: a length inside the water tank alongX-axis (the horizontal direction) of 16 inches, with 19.2 inches alongY-axis (the horizontal direction) and 16 inches in height along Z-axis(the vertical direction). The distances from the ends of the ultrasoundphased transducer arrays 14 a and 14 b to the inside walls of the watertank along X-axis are approximately 3.8425 inches. In one embodiment,the horizontal distance between the front surfaces of the two parallelphased ultrasound transducer arrays can be adjusted from 12 cm to 25 cm,with a 1 cm increment utilizing 14 different sets of spacer blocks. Theaccuracy and precision of the horizontal position is ideally 5 micronsor better. The vertical travel (Z axis) of the two parallel ultrasoundphased transducer arrays 14 a and 14 b is 10 inches from the top surfaceof the water level. The vertical travel step interval can be adjusted toany value, such as 0.25 mm, 0.5 mm, 1 mm, and 2 mm.

In one embodiment, array 14 a, 14 b parameters are as follows: centerfrequency of 1.5 MHz, bandwidth of ˜80% bandwidth (−6 dB) (measured fortwo-way sound propagation energy), the open angle of ultrasound wavesemitting from a single element at ˜80°, with uniform transducer elements16 (<1 dB variation, and uniform bandwidth for one-way sound propagationenergy).

In one embodiment, the arrays 14 a, 14 b comprise 1.5 MHz arrays with384 elements each, equally spaced along the array. In one example, thedimensions/characteristics of the transducer elements are as follows:elevation aperture: 15 mm, element width: 0.4 mm for 1.5 MHz arrays,elevation focus: 10 cm away from the transducer element, with alltransducers configured to be aligned along the array and perpendicularto the elevation plane.

It is appreciated that the above dimensions and configuration detailsare for reference purposes only, and such characteristics may be variedaccordingly.

The advantage of the configuration of scanner 12, over, e.g. the planararrays of FIG. 6, is that the system 10 is using a fewer number oftransducer elements.

B. Dual Parallel Planar Array Scanner

FIG. 6 illustrates a scanner 100 comprising two parallel planar arrays102 a and 102 b aligned opposing each other across the scanning medium44. Arrays 102 a and 102 b each comprise matching grids of 2-D arrays oftransducers 16 (e.g. transducers 16 share the same locations in theirrespective x-z planes shown in FIG. 6). With the planar arrays thescanner 100 generally does not need to be translated in the z (vertical)direction.

There are generally two limitations for the synthetic-aperture breastultrasound tomography with the cylindrical or circular transducerarrays: (a) it is difficult to image the axillary region of the tissue44; and (b) one size of the cylindrical or circular transducer arraywill either be undersized or oversized for most sizes of the breast.

Synthetic-aperture breast ultrasound tomography with two parallel planarultrasound transducer arrays 102 a and 102 b can overcome these twolimitations. As shown in FIG. 6, one planar/2D transducer array 102 bcan be placed close to the axillary region of the tissue 44. Inaddition, the distance between the two planar ultrasound transducerarrays 102 a and 102 b can be adjusted with respect to each other(either manually or with robotic stage 90 as shown in FIG. 5) to fitdifferent sizes of the breast. The ultrasound transducer elements 16 canbe in circular or rectangular shape, and the surface of the transducerelement can be either flat or arc-shaped, as shown in FIG. 8 and FIG. 9.

C. Cylindrical Array Scanner

FIG. 7 shows a cylindrical array scanner 110 having a cylindrical 2-Darray 112 a of transducers 16 in the inside surface of the cylinder wall118 of the ultrasound transducer array. A planar array of elements 112 bmay also be positioned on the bottom surface 116 of the cylinder, whichwould primarily capture backscattered signals.

With the singular cylindrical array scanner 110, a first half of thesemi-cylinder elements 16 will be opposed to or facing the second halfof the semi-cylinder elements 16, and thus be positioned to receivedirect transmission signals 30 (see FIG. 3) at least at varying degreesof angles of incidence. Thus depending on the amount of defocusingwithin each transducer, a plurality, or all, of the non-emittingtransducers 16 will be able to receive a direct transmission signal 30(FIG. 3) (at varying degrees) from the emitting transducer 16, leadingto a full 3D ultrasound tomography image of the breast.

The top end 114 of the cylinder is open, such that the breast tissue 44is immersed into the cylindrical array scanner 110 with 2D ultrasoundtransducer elements 16 surrounding the tissue 44. As with previousembodiments, the ultrasound transducer elements 16 can be in circular orrectangular shape, and the surface of the transducer element can beeither flat or arc-shaped, as shown in FIG. 8 and FIG. 9.

D. Torroidal (Circular) Array Scanner

FIG. 10 shows a torroidal array scanner 120 having a circular array 122of transducers 16 aligned in a ring that is configured to encircle thebreast 44. A robotic stage 124 may be provided to allow for translationof the array 122 to and scan the breast 44 from the chest wall to thenipple region, slice by slice.

With the singular torroidal array scanner 120, a first half of thesemi-circle elements 16 will be opposed to or facing the second half ofthe semi-circle elements 16, and thus be positioned to receive directtransmission signals 30 (see FIG. 3) at least at varying degrees ofangles of incidence. Thus, depending on the amount of defocusing withineach transducer, a plurality, or all, of the non-emitting transducers 16will be able to receive a direct transmission signal 30 (at varyingdegrees) from the emitting transducer 16.

The circular array 122 preferably comprises defocused lens-transducerelements 16 b as shown in FIG. 9, enabling 3-D breast ultrasoundtomography. One advantage of the torroidal configuration 120 is using afewer number of transducer elements compared to the cylindricaltransducer array 110.

E. Dual Torroidal (Circular) Array Scanner

FIG. 11. shows another synthetic-aperture ultrasound breast tomographyscanner 130 that incorporates use of two circular transducer arrays(upper circular array 132 a and lower circular array 132 b).

Image resolution depends, at least in part, on ultrasound illuminationof the target medium 44. To increase the ultrasound out-of-planeillumination angle, an acoustic diverging lens 16 b, as shown in FIG. 9,may be used to widen the elevation beam to the desired level (e.g.between points B anc C in the upper circular array 132 a and D and E inthe lower circular array 132 b (conically diverging beam)). Thus, thedefocused ultrasound transducer elements 16 b transmit ultrasound wavespropagating not only to the transducer elements within the same circulararray, e.g. between B and C in the upper ring 132 a, but also to theother circular transducer array, e.g. between D and E in the lower ring132 b. The upper transducer array 132 a may be configured to scan thebreast 44 from the chest wall position to the nipple region. At eachposition, the lower transducer array 132 b may move to differentvertical position in the z-axis to acquire ultrasound data. Thisconfiguration leads to improved vertical resolution of breast ultrasoundtomography images compared that obtained using one circular transducerarray as shown in FIG. 10.

In practice, the two circular ultrasound transducer arrays 132 a and 132b are immersed into the water tank 76 and both encircle the breast 44.One or both arrays 132 a and 132 b may be configured to translatevertically via a motorized stage 134. For example, during an ultrasoundscan, the upper circular array 132 a can be positioned against the chestwall, while the lower circular array 132 b moves upward from below thenipple region, or vice versa.

As with previous embodiments, each element of one transducer array isfired sequentially, and all elements of both transducer arrays receiveultrasound scattering data 32. The scanner 130 acquires not onlyultrasound propagating from one element to all elements within the sametransducer array, but also those ultrasound waves propagating from theemitting element to all elements of the other transducer array, leadingto a full 3D ultrasound tomography image of the breast.

Such a UST system 130 allows recording of volumetric ultrasound data,and the image resolution limited by slice thickness will be alleviated.In one exemplary design, the data acquisition electronics 18 allow amaximum of 768 parallel channels, so the number of transducers may behalved per array 132 a and 132 b. The coarser sampling in the plane ofthe array will be compensated by the cross illuminations

The scanner 130 of FIG. 11 can significantly improve image resolutionand quality compared to those obtained from an ultrasound tomographysystem with one circular transducer array. A 3D ultrasound tomographysystem 10 of this configuration will be operator independent, which iscritical for cancer screening, and will be more cost-effective than anultrasound tomography system with a cylindrical transducer array.

F. Combination 2D Planar and 2D-Arc Array Scanner

FIG. 12 shows a scanner 140 comprising a semicircular or arcuate array142 b having transducers 16 in an opposing or facing orientation withplanar array 142 a, with target tissue 44 disposed between the two. Thescanner 140 provides a combination of the advantages of the cylindricaltransducer array 110 with those of the 2D planner array 100. Anultrasound tomography system 10 with such combination of transducerarrays improves the range of spatial coverage for data acquisition, andthe planar array 142 can still be placed near the axillary region.

G. Combination 1D Beam and Arc Array Scanner

FIG. 13 illustrates a scanner 150 that reduces the 2D arrays in FIG. 12to 1D arrays (arcuate line array 152 b and linear beam array 152 a).This configuration, using a one-dimensional, straight-phased array 152 aand a 1D arc-shaped array, 152 reduces the number transducers 16, andthus the number of channels required for data acquisition electronics18, while improving the spatial coverage of data acquisition compared towhen using a two parallel phased transducer array scanner 12 in FIG. 5.

II. Synthetic Aperture Ultrasound Tomography Methods

Referring now to FIG. 14, a flow chart of a synthetic apertureultrasound tomography method 200 is shown. This method is preferablyused with any of the systems and scanners shown in FIG. 1 through FIG.14, although other scanning systems are contemplated. Ideally, themethod is used in conjunction with a scanner that has one or more arraysconfigured so that a plurality of transducers 16 of an array, or portionof an array, oppose (at a spaced-apart distance across the targetscanning medium 44) a plurality of transducers 16 of either anotherportion of the array, or a separate array, so that reflection andtransmission data may be acquired with each successive transducerexcitation.

At step 202, the method performs a synthetic aperture ultrasound scan ofthe tissue medium in accordance with the schematic illustration ofscanner 12 FIG. 3. At step 204, reflection and transission data aresimultaneously acquired, as shown in the method 50 of FIG. 4. At step206, ultrasound waveform tomagraphic imaging is performed on theacquired reflection and transmission data to generate a high-resolutionultrasound reconstruction image of the target medium 44.

As mentioned previously, a particular shortcoming of existing ultrasoundomographic imaging is that they either use only transmission data, orreflection data only, for image reconstructions. In contrast, thesynthetic-aperture ultrasound tomography method 200 of the presentinvention acquired both ultrasound transmission and reflection data atthe same time, and use both ultrasound transmission and reflection datafor tomographic reconstructions to greatly improve the shapes andquantitative values of mechanical properties of abnormalities.

FIG. 15 through FIG. 18B demonstrate that using numerical breast-phantomdata from ultrasound waveform tomography using both transmission andreflection data simultaneously significantly improves the accuracy oftomographic reconstructions, compared to those obtained using onlyultrasound transmission data or only ultrasound reflection data.

Numerical phantom data was generated for a synthetic-aperture ultrasoundtomography system with a two parallel phased transducer array scanner 12as shown in FIG. 5. Each transducer array 14 a, 15 b is comprised of 384evenly distributed ultrasound transducer elements, with a pitch size of0.55 mm. The two transducer arrays were separated by 20 cm. Theultrasound source function used is a Ricker wavelet with a centralfrequency of 1.0 MHz.

FIG. 15 shows an image of a numerical breast phantom containing twodifferent tumors (small, light tumor, and larger dark tumor). Thebackground sound-speed of the phantom was 1500 m/s, and those of the twotumor speeds were 1530 m/s and 1550 m/s, respectively. The diameters ofthe tumors were 2.0 mm and 7.0 mm, and approximately 1.3 wavelengths and4.6 wavelengths. The two tumors were positioned along the longitudinaldirection relative to the ultrasound transducer arrays. A high-orderfinite-difference time-domain wave-equation algorithm in accordance withstep 206 was used to compute ultrasound transmission and reflectiondata.

FIG. 16A and FIG. 16B show imaging results (tomographic reconstructionin FIG. 16A, and vertical profile along the center of the tumors in FIG.16B) obtained using only the reflection data. FIG. 17A and FIG. 17B showimaging results (tomographic reconstruction in FIG. 17A, and verticalprofile along the center of the tumors in FIG. 17B) obtained using onlythe transmission data. FIG. 18A and FIG. 18B show imaging results(tomographic reconstruction in FIG. 18A, and vertical profile along thecenter of the tumors in FIG. 18B) obtained using both transmission andreflection data simultaneously in accordance with method 200.

The waveform tomographic reconstruction using only the reflection data(FIG. 16A and FIG. 16B) provides mostly the edge information of thetumors, and can distinguish the two tumors.

On the other hand, the waveform tomographic reconstruction (FIG. 17A andFIG. 17B) using only the transmission data gives mostly lowspatial-wavenumber components of the tumors, and it is almost impossibleto separate the two tumors.

By contrast, the waveform tomographic reconstruction using both thetransmission and reflection data simultaneously (FIG. 18A and FIG. 18B)takes the advantages of the above two kinds of tomographicreconstructions, and produces an image with much improved tumor edgesand sound-speed reconstructions.

A. Synthetic Aperture Ultrasound with Waveform Tomography Inversion

FIG. 19 illustrates a preferred method 206 for generating the ultrasoundwaveform step of method 200 (FIG. 14) using both transmission andreflection data for ultrasound waveform tomography. As shown in FIG. 19,reflection and transmission data are input at step 210, and rayapproximation is performed at step 212 to generate an initial model.Next at step 214, image reconstruction is performed by computing thewave acoustic wave properties of the data by calculating the mean squaredifference between the observed and synthetic waveforms. In particular,step 214 is performed by performing iterative waveform inversion withregularization, as will be explained in further detail below. From amore basic level, performing step 214 is achieved by solving theacoustic wave equation of Eq. 1 with the minimization model of Eq. 2,described in more detail below.

The acoustic-wave equation in the time domain is given by:

$\begin{matrix}{{{\lbrack {{\frac{1}{K(r)}\frac{\partial^{2}}{\partial t^{2}}} - {\nabla( {\frac{1}{\rho(r)}\nabla} )}} \rbrack{p( {r,t} )}} = {{s(t)}{\delta( {r - r_{0}} )}}},} & {{Eq}.\mspace{14mu} 1}\end{matrix}$where ρ(r) is the density, K(r) is the bulk modulus, s(t) is the sourceterm, r₀ is the source location, and p(r,t) is the pressure field.

The inverse problem of Eq. 1, or waveform tomography, can be posed as aminimization problem such that:

$\begin{matrix}{{{E(m)} = {\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{s}( {m,t} )}} \rbrack^{2}{dt}}}}}},} & {{Eq}.\mspace{14mu} 2}\end{matrix}$where E(m) is the misfit function, d represents recorded waveforms,which can be either reflection data, or transmission data, or combinedreflection and transmission data, s is the source index, N_(s) is thenumber of sources, and m is the model parameter.

The minimization operation in Eq. 2 is to find a model m that yields theminimum difference between observed and synthetic waveforms. The modelparameter m is given by:

$\begin{matrix}{{m = \begin{bmatrix}{V\mspace{14mu}{or}\mspace{14mu} K} \\\rho\end{bmatrix}},} & {{Eq}.\mspace{14mu} 3}\end{matrix}$where V=√{square root over (K/ρ)} is the acoustic wave-speed.

A typical approach to minimize the misfit function is the gradient-basedmethod, e.g. the steepest descend or the conjugate gradient methods(NCG). In each step, the model first evaluates the gradient of themisfit function at the current model, and then determines a searchdirection based on the current gradient or previous gradients. Thesearch direction for the misfit function of acoustic wave is written as:

$\begin{matrix}{{\gamma_{k}\text{∼}{\sum\limits_{s = 1}^{N_{s}}{\int_{t}\;{{u_{s}( {x,{t;m_{k}}} )}{b_{s}( {x,{t;m_{k}}} )}{dt}}}}},} & {{Eq}.\mspace{14mu} 4}\end{matrix}$where γ is the search direction, k the iteration number, u the forwardpropagated wavefield, b the backward propagated wavefield, x the spatialvariable, t the temporal variable. The step length is preferably foundby a line search method. The model is updated along the search directionusing the step length:m _(k+1) =m _(k)+αγ_(k),  Eq. 5where α is the step length. This process is repeated iteratively until acertain convergence criterion is satisfied.

Although the resolve power of ultrasound waveform tomography isappealing, it is computationally expensive. The computational costincreases linearly with the number of sources, because the searchdirection γ and the step length α are both needed to be evaluated fromevery source, as shown in Eq. 4 and Eq. 5. As the number of sourcesincreases, ultrasound waveform tomography becomes very time-consuming,particularly for synthetic-aperture ultrasound tomography, where thesystem usually consists of hundreds to thousands of transducer elements.

The following description details two methods for increasing efficiencyin computations for ultrasound waveform tomography. First, the sourceencoding method of the present invention will be discussed. Then, thedata blending method of the present invention will be discussed.

i. Ultrasound Waveform Tomography with Source Encoding

For source encoding, the misfit function may be modified according to:

$\begin{matrix}{{{E^{\prime}(m)} = {\min\limits_{m}{\sum\limits_{g = 1}^{N_{g}}{\int{\{ {\sum\limits_{s = 1}^{n_{g}}\lbrack {{d_{g,s}(t)} - {p_{g,s}( {m,t} )}} \rbrack} \}^{2}{dt}}}}}},} & {{Eq}.\mspace{14mu} 6}\end{matrix}$where d_(g,s) and p_(g,s) are respectively data and simulated waveformsfor the s^(th) source within the g^(th) encoding group, N_(g) is thenumber of groups, and n_(g) is the number of sources encoded in theg^(th) group such that

$N_{s} = {\sum\limits_{g = 1}^{N_{g}}{n_{g}.}}$

The misfit function in Eq. 6 can be calculated in only one simulation,because of the linearity of the acoustic wave equation. However, Eq. 6is not equivalent to Eq. 2, because Eq. 6 contains the cross-terms ofdifferent sources, which can be seen by simply expanding Eq. 6.

The source encoding technique of the present invention is used to reducethe cross-terms used in waveform tomography. Referring to FIG. 20, thesource encoding method 220 assigns every source (e.g. transducers 16 inFIG. 1) with a phase as a source signature (step 224), and launchesmultiple sources simultaneously in a single simulation (step 226). Thesearch direction may then be calculated via Eq. 4 using the encodedsources (step 228).

In a preferred embodiment, the number of sources is first divided intogroups at step 222, such that a partial search direction is calculatedat step 228, and the search directions of all groups are summed at step230.

In a preferred embodiment, the phases were randomly selected at step224.

Source encoding method 220 is preferrably applied to ultrasound waveformtomography using both transmission and reflection data from asynthetic-aperture ultrasound tomography system (e.g. any of the systemsembodied in FIGS. 1-14 above). However, it is appreciated that thismethod may be applied to any systems and data, whether the data istransmission only or reflection only.

Accordingly, the misfit function is given by:

$\begin{matrix}{{E^{\prime}(m)} = {{\min\limits_{m}{\sum\limits_{s = 1}^{Ns}{\int{\lbrack {{\overset{\_}{d}}_{s} - {\overset{\_}{p}}_{s}} \rbrack^{2}{dt}}}}} + {\sum\limits_{g = 1}^{N_{g}}{\sum\limits_{s = 1}^{n_{g}}{\sum\limits_{{s^{\prime} = 1},{s^{\prime} \neq s}}^{n_{g}}{\int{{\lbrack {{\overset{\_}{d}}_{g,s} - {\overset{\_}{p}}_{g,s}} \rbrack\lbrack {{\overset{\_}{d}}_{g,s^{\prime}} - {\overset{\_}{p}}_{g,s^{\prime}}} \rbrack}{{dt}.}}}}}}}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$where p is the encoded synthetic waveform, and d is the encoded data,which may be either transmission data, reflection data, or combinedreflection and transmission data.

Eq. 7 and Eq. 2 are equivalent if the cross-term in Eq. 7 can beremoved. The encoded waveform and data are given by:d _(g,s) =d _(g,s)×ψ_(g,s),p _(g,s) =p _(g,s)×ψ_(g,s),  Eq. 8where ψ is a random phase or phase value. In a method of performingwaveform tomography inversion according to the present invention, thisphase value is added to the source and data during numerical simulationsof forward wave propagation from sources and backward propagation ofultrasound wavefields from receivers.

Algorithm 1 below shows an implementation ultrasound waveform tomographyin accordance with the source encoding 220 shown in FIG. 20, where TOLis the input tolerance for the iteration, and m⁽⁰⁾ is the input model.

Algorithm 1 Ultrasound waveform tomography using source encoding Input:m⁽⁰⁾ , TOL Output: m^((k)) 1: Separate N_(s) sources into N_(g) groups(step 222) 2: Initialize k = 0, γ₀; 3: while {||γ_(k)|| > TOL } do 4:for g=1, N_(g) 5: Apply a random phase to each source and correspondingdata within  g^(th) group (step 224); 6: Start all the sources withing^(th) group (step 226) 7:  Calculate partial search direction (Eq. 4)using the encoded sources   and data in g^(th) group ; 8:  end do9:  Sum up the partial search directions of all the groups to   obtainγ_(k) (step 230); 10: Update model m^((k)) (Eq.5) ; 11: k ← k + 1; 12:end while

ii. Ultrasound Waveform Tomography with Data Blending

For data blending, the misfit function may be modified according to:

$\begin{matrix}{{{E^{\prime}(m)} = {\min\limits_{m}{\sum\limits_{g = 1}^{N_{g}}{\int{\{ {\sum\limits_{s = 1}^{n_{g}}\lbrack {{d_{g,s}(t)} - {p_{g,s}( {m,t} )}} \rbrack} \}^{2}{dt}}}}}},} & {{Eq}.\mspace{14mu} 9}\end{matrix}$where d_(g,s) and p_(g,s) are respectively data and simulated waveformsfor the s^(th) source within the g^(th) blending group, N_(g) is thenumber of groups, and n_(g) is the number of sources blended in theg^(th) group such that

$N_{s} = {\sum\limits_{g = 1}^{N_{g}}{n_{g}.}}$

The misfit function in Eq. 6 can be calculated in only one simulation,because of the linearity of the acoustic wave equation. However, the Eq.6 is not equivalent to Eq. 2, because Eq. 6 contains the cross-terms ofdifferent sources, which can be seen by simply expanding Eq. 6.

The data blending technique of the present invention is used to reducethe cross-terms used in waveform tomography. Referring to FIG. 21, thedata blending method 250 applies a random delay time to each source(e.g. transducers 16 in FIG. 1) and corresponding data (step 254), andlaunches or excites multiple sources simultaneously in a singlesimulation (step 256). The search direction may then be calculated viaEq. 4 using the blended sources (step 258).

In a preferred embodiment, the number of sources is first divided intogroups at step 252, such that a partial search direction is calculatedat step 258, and the search directions of all groups are summed at step260.

In a preferred embodiment, the phases were randomly selected at step254.

Data blending method 250 is preferrably applied to ultrasound waveformtomography using both transmission and reflection data from asynthetic-aperture ultrasound tomography system (e.g. any of the systemsembodied in FIG. 1 through FIG. 14 above). However, it is appreciatedthat this method may be applied to any systems and data, whether thedata is transmission only or reflection only.

Accordingly, the misfit function is given by:

$\begin{matrix}{{E^{\prime}(m)} = {{\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{s}( {m,t} )}} \rbrack^{2}{dt}}}}} + {\sum\limits_{g = 1}^{N_{g}}{\sum\limits_{s = 1}^{n_{g}}{\sum\limits_{{s^{\prime} = 1},{s^{\prime} \neq s}}^{n_{g}}{\int{{\lbrack {{d_{g,s}(t)} - {p_{g,s}( {m,t} )}} \rbrack\lbrack {{d_{g,s^{\prime}}(t)} - {p_{g,s^{\prime}}( {m,t} )}} \rbrack}{{dt}.}}}}}}}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$where p is the encoded synthetic waveform, and d is the encoded data,which may be either transmission data, reflection data, or combinedreflection and transmission data.

During simulations in inversion, we add a random time delay t_(s) toeach common-transmitter dataset and the corresponding forwardpropagation wavefield from the transmitting transducer element (source),so we have:d _(g,s)(t)=∫d _(g,s)(ω)e ^(iω(t+t) ^(g,s) ⁾ dω,p _(g,s)(t)=∫p _(g,s)(ω)e ^(iω(t+t) ^(g,s) ⁾ dω,  Eq. 11where ω is the frequency, t_(g,s) is the delay time for source s withinthe g^(th) group. In a method of performing waveform tomographyinversion according to the present invention, this time delay is addedto the source and data during numerical simulations of forward wavepropagation from sources and backward propagation of ultrasoundwavefields from receivers.

In the frequency domain, dropping all the variables, E and E′ withblended sources can be written as:

$\begin{matrix}{\mspace{79mu}{{{E(m)} = {\min\limits_{m}\{ {\sum\limits_{s = 1}^{N_{s}}{{\lbrack {d_{s} - p_{s}} \rbrack\lbrack {d_{s} - p_{s}} \rbrack}^{*}d\;\omega}} \}}},}} & {{Eq}.\mspace{14mu} 12} \\{\mspace{79mu}{and}} & \; \\{{E^{\prime}(m)} = {{\min\limits_{m}{\sum\limits_{s = 1}^{Ns}{\int{{\lbrack {{\overset{\_}{d}}_{s} - {\overset{\_}{p}}_{s}} \rbrack\lbrack {{\overset{\_}{d}}_{s} - {\overset{\_}{p}}_{s}} \rbrack}^{*}d\;\omega}}}} + {\sum\limits_{g = 1}^{N_{g}}{\sum\limits_{s = 1}^{n_{g}}{\sum\limits_{{s^{\prime} = 1},\;{s^{\prime} \neq s}}^{n_{g}}{\int{{\lbrack {{\overset{\_}{d}}_{g,s} - {\overset{\_}{p}}_{g,s}} \rbrack\lbrack {{\overset{\_}{d}}_{g,s^{\prime}} - {\overset{\_}{p}}_{g,s^{\prime}}} \rbrack}^{*}d\;{\omega.}}}}}}}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

Substituting Eq. 10 into Eq. 8, we get:

$\begin{matrix}{{E^{\prime}(m)} = {{E(m)} + {\sum\limits_{g = 1}^{N_{g}}{\sum\limits_{s = 1}^{n_{g}}{\sum\limits_{{s^{\prime} = 1};\;{s^{\prime} \neq s}}^{n_{g}}{\int{{\lbrack {d_{g,s} - p_{g,s}} \rbrack\lbrack {d_{g,s^{\prime}} - p_{g,s^{\prime}}} \rbrack}^{*}e^{i\;{\omega{({t_{g,s} - t_{g,s^{\prime}}})}}}d\;{\omega.}}}}}}}} & {{Eq}.\mspace{14mu} 14}\end{matrix}$

Generally, the second term in Eq. 14 does not vanish. If we choose t_(s)and t_(s′) randomly, the first term in equation Eq. 14 is not affected,but the second term changes in each iteration step. As the number ofiterations increases, the influence of the first term in thereconstruction accumulates, while the influence of the second termgradually reduces.

Algorithm 2 below shows an implementation ultrasound waveform tomographyin accordance with the source encoding 250 shown in FIG. 21, where TOLis the input tolerance for the iteration, and m⁽⁰⁾ is the input model.

Algorithm 2 Ultrasound waveform tomography using data blending Input:m⁽⁰⁾ , TOL Output: m^((k)) 1: Separate N_(s) sources and thecorresponding data into N_(g) groups  (step 252) 2: Initialize k = 0,γ₀; 3: while {||γ_(k)|| > TOL } do 4: for g=1, N_(g) 5: Apply a randomdelay-time to each source (step 254) and corresponding  data withing^(th) group; 6: Start all the sources within g^(th) group (step 256);7: Calculate partial search direction using the blended sources and data in g^(th) group (step 258); 8: end do 9: Sum up the partial searchdirections of all the groups to obtain   y_(k) (step 260); 10: Updatemodel m^((k)) (Eq. 5); 11: k ← k + 1; 12: end while

Tests were conducted to evaluate the source encoding method 220 (FIG.20) and the data blending method 250 (FIG. 21) of the present invention.

To validate the source encoding method 220 for ultrasound waveformtomography a numerical breast phantom was scanned using asynthetic-aperture ultrasound tomography system with two parallel phasedtransducer arrays similar to the scanner configuration 12 of FIG. 5. Thenumerical breast phantom contained two breast tumors located near thecenter of the imaging region, as shown in FIG. 22. One of the tumors hasa diameter of 2.2 mm, the other has a diameter of 3.3 mm. The breasttumors are positioned along the transverse direction relative to thetransducer arrays.

The waveform inversion result for ultrasound waveform tomography oftransmission and reflection data without using source encoding is shownin FIG. 23A and FIG. 23B. The location and the sound speed of the twosmall tumors are fully reconstructed. FIG. 23A and FIG. 23B are used asa reference to compare with the results obtained using ultrasoundwaveform tomography with source encoding.

In one simulation, 4, 8, 12, and 24 sources were encoded. Therefore, thecomputational times are one forth, one eighth, one twelfth and onetwenty-fourth of that for the original ultrasound waveform tomography.The inversion results of the four different groupings after 20iterations are almost identical, as shown in FIG. 24A through FIG. 24D.

The horizontal profiles of FIG. 24A through FIG. 24D at the verticallocation of 91 mm also show that the four different groupings givesimilar reconstruction results. The boundary of the larger tumor on theright is a little blurred when using 24 sources in one simulation (seethe horizontal locations at 120 mm and 122 mm in FIG. 25A through FIG.25D).

Combining encoded data from multiple sources in one simulation resultsin a few image artifacts, as can be seen in FIG. 24A through FIG. 24Dand FIG. 25A through FIG. 25D.

Ultrasound waveform tomography with source encoding not only producesalmost the same reconstruction results as the original ultrasoundwaveform tomography, but also keeps the convergence rate unchanged.

The results at the third iteration of the four different groupingsexplain the process during inversion (see FIG. 26A through FIG. 26D).Again, the profiles in FIG. 26A through FIG. 26D are similar to oneanother. More encoded sources used in one simulation only produceslightly more image noise than those obtained using fewer encodedsources (from 114 mm to 119 mm in FIG. 6). The image noise is weaker atthe locations where the tumors present (from 111 mm to 113 mm in FIG.6). This implies that the source encoding successfully eliminates theinterference among different sources in one simulation. After manyiteration steps, the artifact caused by the cross-interference amongdifferent sources is further reduced (FIG. 25A through FIG. 25D).

To validate the data blending method 250 for ultrasound waveformtomography, a numerical breast phantom was scanned using asynthetic-aperture ultrasound tomography system with two parallel phasedtransducer arrays similar to the scanner configuration 12 of FIG. 5. Theimaging region had a length of 211 mm and a width of 200 mm. 384transducer elements were placed along the two parallel transducerarrays. The central frequency of ultrasound was 1 MHz. The phantom had abackground sound speed of 1500 m/s.

The numerical breast phantom contained two breast tumors located nearthe center of the imaging region, as shown in FIG. 27. One of the tumorshas a diameter of 2.2 mm, the other has a diameter of 3.3 mm. The breasttumors are positioned along the transverse direction relative to thetransducer arrays.

The waveform inversion result for ultrasound waveform tomography oftransmission and reflection data without using source encoding is shownin FIG. 28A and FIG. 28B. The location and the sound speed of the twosmall tumors are fully reconstructed. FIG. 28A and FIG. 28B are used asa reference to compare with the results obtained using ultrasoundwaveform tomography with source encoding.

In one simulation, synthetic-aperture ultrasound data from 4, 8, and 24sources in were blended. The computational times of ultrasound waveformtomography with blending data are about one forth, one eighth, onetwelfth and one twenty-fourth of that for the original ultrasoundwaveform tomography without data blending. We used three differentmaximum delay times in our numerical examples: one period, ½ periods and¼ periods, to study the effect of the maximum time delay used in blendeddata.

The ultrasound waveform tomography results of the three differentdata-blending schemes with three different maximum delay times after 20iterations are almost identical (FIG. 29A through FIG. 29C). Usingmultiple sources in one simulation leads to only a few image artifactscompared with the result obtained using the original waveform tomographywithout data blending (FIG. 28A and FIG. 28B). These image artifacts areseen more clearly from the horizontal profiles in FIG. 30A through FIG.30C, FIG. 32A through FIG. 32C, and FIG. 34A through FIG. 34C, whichcorrespond to the waveform tomography results of FIG. 29A through FIG.29C, FIG. 31A through FIG. 31C, and FIG. 33A through FIG. 33C.

When using the same maximum delay time, more sources are blendedtogether, the stronger the artifacts, especially within the larger tumor(see the horizontal locations at 120 mm and 122 mm in FIG. 30A throughFIG. 30C, FIG. 32A through FIG. 32C, and FIG. 34A through FIG. 34C).

When the maximum delay time decreases, the artifacts generally increase.The effects are observed more clearly when more sources are blendedtogether (see FIG. 30C, FIG. 32C, and FIG. 34C). If fewer sources areblended together, decreasing the maximum delay time does not change thereconstruction result significantly (see FIG. 30A, FIG. 32A, and FIG.34A). This result suggests that a longer delay time needs to be usedwhen data from more sources are blended together.

The data blending in ultrasound waveform tomography not only results intomography results as good as that of the original ultrasound waveforminversion, but also keeps the convergence rate unchanged. Theconvergence rates in our numerical examples of ultrasound waveformtomography with blending data are the same as that of the originalwaveform tomography without data blending. This suggests that the datablending approach is very efficient to reduce the interference betweendifferent sources within a few iteration steps. Therefore, data blendingserves as a powerful tool to significantly reduce the computational costof ultrasound waveform tomography.

Ultrasound waveform tomography methods using source encoding and datablending were generated, and both validated the method using ultrasoundtransmission and reflection data from a synthetic-aperture ultrasoundtomography systems. The results show that the source encoding and datablending both dramatically improve the computational efficiency ofultrasound waveform inversion by simulating the wavefields of multiplesources at the same time during inversion. The computational cost is oneto two orders of magnitudes less than that for the original waveformtomography.

The source encoding technique significantly reduces thecross-interference among different sources in one simulation byassigning a random phase signature to every source and its common-sourcedata. The reconstructed image obtained using the source encoding isalmost identical to that obtained using the original waveformtomography. Meanwhile, the convergence rate of ultrasound waveformtomography with source encoding is unchanged from the originalultrasound waveform tomography. Our numerical examples show thatultrasound waveform tomography with source encoding is feasible forfuture clinical applications.

In summary, the synthetic-aperture ultrasound tomography systems andmethods of the present invention acquire ultrasound transmission andreflection data at the same time, and we have demonstrated thatultrasound waveform tomography using either source endocing or datablending greatly improves computational efficiency, leading to a reducedcomputation cost that is less than one tenth of the computational costfor the original ultrasound waveform tomography.

From the discussion above it will be appreciated that the invention canbe embodied in various ways, including the following:

1. An ultrasound tomography imaging method for imaging a tissue mediumwith one or more ultrasound transducer arrays comprising a plurality oftransducers, wherein said transducers comprise source transducers,receiving transducers, or both, the method comprising: assigning a phasevalue to the plurality of source transducers; exciting the plurality oftransducers; and calculating a search direction based on data relatingto the excited plurality of transducers.

2. A method as recited in any of the preceding embodiments, wherein thephase value is randomly assigned.

3. A method as recited in any of the preceding embodiments, wherein saidphase value functions a source signature between different sourcetransducers.

4. A method as recited in any of the preceding embodiments, wherein saidphase value reduces cross interference produced by different sourcetransducers.

5. A method as recited in any of the preceding embodiments, furthercomprising: performing numerical waveform inversion to generate anultrasound waveform tomography image reconstruction; wherein said phasevalues are assigned during the numerical waveform inversion.

6. A method as recited in any of the preceding embodiments, wherein theimage reconstruction comprises calculating forward wavefield propagationfrom transducer sources and backward wavefield propagation of fromultrasound receivers.

7. A method as recited in any of the preceding embodiments, wherein theimage reconstruction further comprises: exciting a first transducerwithin plurality of transducers to generate an ultrasound field withinthe tissue medium; acquiring a transmission signal and a reflectionsignal from a second transducer within the one or more ultrasoundtransducer arrays; and generating an ultrasound waveform tomographyimage reconstruction using both the acquired reflection and transmissionsignals.

8. A method as recited in any of the preceding embodiments, wherein saidimage reconstruction is a function of computing an acoustic waveproperty of the reflection and transmission signals by calculating aminimum mean square difference between observed and synthetic waveformsrelating to the reflection and transmission signals.

9. A method as recited in any of the preceding embodiments, wherein saidimage reconstruction is a function of:

${{E(m)} = {\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{s}( {m,t} )}} \rbrack^{2}{dt}}}}}},$where E(m) is the misfit function, d is recorded waveforms, s is thesource index, N_(s) is the number of sources, and m is the modelparameter.

10. A method as recited in any of the preceding embodiments, wherein therecorded waveforms comprise either reflection data or transmission datafrom the transducers.

11. A method as recited in any of the preceding embodiments, wherein therecorded waveforms comprise reflection and transmission data from thetransducers.

12. A method as recited in any of the preceding embodiments, wherein thesearch direction is used in calculating a gradient of the misfitfunction.

13. A method as recited in any of the preceding embodiments, wherein thesearch direction is calculated according to:

${\gamma_{k}\text{∼}{\sum\limits_{s = 1}^{N_{s}}{\int_{t}{{u_{s}( {x,{t;m_{k}}} )}{b_{s}( {x,{t;m_{k}}} )}{dt}}}}},$where γ is the search direction, k the iteration number, u is a forwardpropagated wavefield, b is a backward propagated wavefield, x is aspatial variable, and t is a temporal variable.

14. An ultrasound tomography imaging system for imaging a tissue mediumwith one or more ultrasound transducer arrays comprising a plurality oftransducers, wherein said transducers comprise source transducers,receiving transducers, or both, said the system comprising: a processor;and programming executable on said processor and configured for:assigning a phase value to the plurality of source transducers; excitingthe plurality of transducers; and calculating a search direction basedon data relating to the excited plurality of transducers.

15. A system as recited in any of the preceding embodiments, wherein thephase value is randomly assigned.

16. A system as recited in any of the preceding embodiments, phase valuefunctions a source signature between different source transducers.

17. A system as recited in any of the preceding embodiments, whereinsaid phase value reduces cross interference produced by different sourcetransducers.

18. A system as recited in any of the preceding embodiments: whereinsaid programming is further configured for performing numerical waveforminversion to generate an ultrasound waveform tomography imagereconstruction; wherein said phase values are assigned during thenumerical waveform inversion.

19. A system as recited in any of the preceding embodiments, wherein theimage reconstruction comprises calculating forward wavefield propagationfrom transducer sources and backward wavefield propagation of fromultrasound receivers.

20. A system as recited in any of the preceding embodiments, wherein theimage reconstruction further comprises: exciting a first transducerwithin plurality of transducers to generate an ultrasound field withinthe tissue medium; acquiring a transmission signal and a reflectionsignal from a second transducer within the one or more ultrasoundtransducer arrays; and generating an ultrasound waveform tomographyimage reconstruction using both the acquired reflection and transmissionsignals.

21. A system as recited in any of the preceding embodiments, whereinsaid image reconstruction is a function of computing an acoustic waveproperty of the reflection and transmission signals by calculating aminimum mean square difference between observed and synthetic waveformsrelating to the reflection and transmission signals.

22. A system as recited in any of the preceding embodiments, whereinsaid image reconstruction is a function of:

${{E(m)} = {\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{s}( {m,t} )}} \rbrack^{2}{dt}}}}}},$where E(m) is the misfit function, d is recorded waveforms, s is thesource index, N_(s) is the number of sources, and m is the modelparameter.

23. A system as recited in any of the preceding embodiments, wherein therecorded waveforms comprise either reflection data or transmission datafrom the transducers.

24. A system as recited in any of the preceding embodiments, wherein therecorded waveforms comprise reflection and transmission data from thetransducers.

25. A system as recited in any of the preceding embodiments, wherein thesearch direction is used in calculating a gradient of the misfitfunction.

26. A system as recited in any of the preceding embodiments, wherein thesearch direction is calculated according to:

${\gamma_{k}\text{∼}{\sum\limits_{s = 1}^{N_{s}}{\int_{t}{{u_{s}( {x,{t;m_{k}}} )}{b_{s}( {x,{t;m_{k}}} )}{dt}}}}},$where γ is the search direction, k the iteration number, u the forwardpropagated wavefield, b the backward propagated wavefield, x the spatialvariable, t the temporal variable.

27. An ultrasound tomography imaging method for imaging a tissue mediumwith one or more ultrasound transducer arrays comprising a plurality oftransducers, wherein said transducers comprise source transducers,receiving transducers, or both, the method comprising: assigning a timedelay to the plurality of source transducers; exciting the plurality oftransducers; and calculating a search direction based on data relatingto the excited plurality of transducers.

28. A method as recited in any of the preceding embodiments, wherein thetime delay is randomly assigned.

29. A method as recited in any of the preceding embodiments, wherein thetime delay functions a source signature between different sourcetransducers.

30. A method as recited in any of the preceding embodiments, wherein thetime delay reduces cross interference produced by different sourcetransducers.

31. A method as recited in any of the preceding embodiments, furthercomprising: performing numerical waveform inversion to generate anultrasound waveform tomography image reconstruction; wherein said phasevalues are assigned during the numerical waveform inversion.

32. A method as recited in any of the preceding embodiments, wherein theimage reconstruction comprises calculating forward wavefield propagationfrom transducer sources and backward wavefield propagation of fromultrasound receivers.

33. A method as recited in any of the preceding embodiments, wherein theimage reconstruction further comprises: exciting a first transducerwithin plurality of transducers to generate an ultrasound field withinthe tissue medium; acquiring a transmission signal and a reflectionsignal from a second transducer within the one or more ultrasoundtransducer arrays; and generating an ultrasound waveform tomographyimage reconstruction using both the acquired reflection and transmissionsignals.

34. A method as recited in any of the preceding embodiments, whereinsaid image reconstruction is a function of computing an acoustic waveproperty of the reflection and transmission signals by calculating aminimum mean square difference between observed and synthetic waveformsrelating to the reflection and transmission signals.

35. A method as recited in any of the preceding embodiments, whereinsaid image reconstruction is a function of:

${{E(m)} = {\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{s}( {m,t} )}} \rbrack^{2}{dt}}}}}},$where E(m) is the misfit function, d is recorded waveforms, s is thesource index, N_(s) is the number of sources, and m is the modelparameter.

36. A method as recited in any of the preceding embodiments, wherein therecorded waveforms comprise either reflection data or transmission datafrom the transducers.

37. A method as recited in any of the preceding embodiments, wherein therecorded waveforms comprise reflection and transmission data from thetransducers.

38. A method as recited in any of the preceding embodiments, wherein thesearch direction is used in calculating a gradient of the misfitfunction.

39. A method as recited in any of the preceding embodiments, wherein thesearch direction is calculated according to:

${\gamma_{k}\text{∼}{\sum\limits_{s = 1}^{N_{s}}{\int_{t}{{u_{s}( {x,{t;m_{k}}} )}{b_{s}( {x,{t;m_{k}}} )}{dt}}}}},$where γ is the search direction, k the iteration number, u is a forwardpropagated wavefield, b is a backward propagated wavefield, x is aspatial variable, and t is a temporal variable.

40. An ultrasound tomography imaging system for imaging a tissue mediumwith one or more ultrasound transducer arrays comprising a plurality oftransducers, wherein said transducers comprise source transducers,receiving transducers, or both, the system comprising: a processor; andprogramming executable on said processor and configured for: assigning atime delay to the plurality of source transducers; exciting theplurality of transducers; and calculating a search direction based ondata relating to the excited plurality of transducers.

41. A system as recited in any of the preceding embodiments, wherein thetime delay is randomly assigned.

42. A system as recited in any of the preceding embodiments, wherein thetime delay functions a source signature between different sourcetransducers.

43. A system as recited in any of the preceding embodiments, wherein thetime delay reduces cross interference produced by different sourcetransducers.

44. A system as recited in any of the preceding embodiments: whereinsaid programming is further configured for performing numerical waveforminversion to generate an ultrasound waveform tomography imagereconstruction; wherein said phase values are assigned during thenumerical waveform inversion.

Embodiments of the present invention may be described with reference toflowchart illustrations of methods and systems according to embodimentsof the invention, and/or algorithms, formulae, or other computationaldepictions, which may also be implemented as computer program products.In this regard, each block or step of a flowchart, and combinations ofblocks (and/or steps) in a flowchart, algorithm, formula, orcomputational depiction can be implemented by various means, such ashardware, firmware, and/or software including one or more computerprogram instructions embodied in computer-readable program code logic.

As will be appreciated, any such computer program instructions may beloaded onto a computer, including without limitation a general purposecomputer or special purpose computer, or other programmable processingapparatus to produce a machine, such that the computer programinstructions which execute on the computer or other programmableprocessing apparatus create means for implementing the functionsspecified in the block(s) of the flowchart(s).

Accordingly, blocks of the flowcharts, algorithms, formulae, orcomputational depictions support combinations of means for performingthe specified functions, combinations of steps for performing thespecified functions, and computer program instructions, such as embodiedin computer-readable program code logic means, for performing thespecified functions. It will also be understood that each block of theflowchart illustrations, algorithms, formulae, or computationaldepictions and combinations thereof described herein, can be implementedby special purpose hardware-based computer systems which perform thespecified functions or steps, or combinations of special purposehardware and computer-readable program code logic means.

Furthermore, these computer program instructions, such as embodied incomputer-readable program code logic, may also be stored in acomputer-readable memory that can direct a computer or otherprogrammable processing apparatus to function in a particular manner,such that the instructions stored in the computer-readable memoryproduce an article of manufacture including instruction means whichimplement the function specified in the block(s) of the flowchart(s).The computer program instructions may also be loaded onto a computer orother programmable processing apparatus to cause a series of operationalsteps to be performed on the computer or other programmable processingapparatus to produce a computer-implemented process such that theinstructions which execute on the computer or other programmableprocessing apparatus provide steps for implementing the functionsspecified in the block(s) of the flowchart(s), algorithm(s), formula(e),or computational depiction(s).

Although the description herein contains many details, these should notbe construed as limiting the scope of the disclosure but as merelyproviding illustrations of some of the presently preferred embodiments.Therefore, it will be appreciated that the scope of the disclosure fullyencompasses other embodiments which may become obvious to those skilledin the art.

In the claims, reference to an element in the singular is not intendedto mean “one and only one” unless explicitly so stated, but rather “oneor more.” All structural, chemical, and functional equivalents to theelements of the disclosed embodiments that are known to those ofordinary skill in the art are expressly incorporated herein by referenceand are intended to be encompassed by the present claims. Furthermore,no element, component, or method step in the present disclosure isintended to be dedicated to the public regardless of whether theelement, component, or method step is explicitly recited in the claims.No claim element herein is to be construed as a “means plus function”element unless the element is expressly recited using the phrase “meansfor”. No claim element herein is to be construed as a “step plusfunction” element unless the element is expressly recited using thephrase “step for”.

What is claimed is:
 1. An ultrasound tomography imaging method forimaging a tissue medium with one or more ultrasound transducer arrayscomprising a plurality of transducers, the method comprising: assigninga plurality of different phase values to a plurality of at least threedifferent source transducers of the plurality of transducers; excitingthe at least three source transducers in accordance with the assigneddifferent phase values to generate a plurality of ultrasound waveformswithin the tissue medium; receiving data from a plurality of receivingtransducers of the plurality of transducers in accordance withtransmissions and reflections of the plurality of ultrasound waveformswithin the tissue medium; and calculating a search direction based ondata from the receiving transducers, wherein the method furthercomprises performing a numerical simulation of forward propagation ofwavefields from the source transducers and backward propagation ofwavefields from the receiving transducers, wherein the calculating thesearch direction is based on the forward propagation of wavefields andthe backward propagation of wavefields, and wherein the method furthercomprises: updating a model based on the search direction; computing anultrasound waveform tomography image reconstruction in accordance withthe updated model; and performing numerical waveform inversion togenerate the ultrasound waveform tomography image reconstruction,wherein the plurality of different phase values are assigned during thenumerical waveform inversion.
 2. The ultrasound tomography imagingmethod of claim 1, further comprising: receiving a transmission signaland a reflection signal at one of the receiving transducers within theone or more ultrasound transducer arrays; and generating an ultrasoundwaveform tomography image reconstruction using the data received inaccordance with the transmission signal and the reflection signal.
 3. Anultrasound tomography imaging method for imaging a tissue medium withone or more ultrasound transducer arrays comprising a plurality oftransducers, the method comprising: assigning a plurality of differentphase values to a plurality of at least three different sourcetransducers of the plurality of transducers; exciting the at least threesource transducers in accordance with the assigned different phasevalues to generate a plurality of ultrasound waveforms within the tissuemedium; receiving data from a plurality of receiving transducers of theplurality of transducers in accordance with transmissions andreflections of the plurality of ultrasound waveforms within the tissuemedium; and calculating a search direction based on data from thereceiving transducers, wherein the method further comprises performing anumerical simulation of forward propagation of wavefields from thesource transducers and backward propagation of wavefields from thereceiving transducers, wherein the calculating the search direction isbased on the forward propagation of wavefields and the backwardpropagation of wavefields, wherein the method further comprises:updating a model based on the search direction; and computing anultrasound waveform tomography image reconstruction in accordance withthe updated model, and wherein the ultrasound wave tomography imagereconstruction is a function of:${{E(m)} = {\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{S}( {m,t} )}} \rbrack^{2}dt}}}}},$where E(m) is a misfit function, d is one of transmission data andreflection data, p is a simulated waveform from the numericalsimulation, s is a source index indicating one of the sourcetransducers, N_(s) is the number of source transducers, and m is a modelparameter of the model.
 4. An ultrasound tomography imaging system forimaging a tissue medium comprising: two or more ultrasound transducerarrays spaced apart from each other, each of the ultrasound transducerarrays comprising a plurality of transducers; a processor; and memorystoring instructions that, when executed by the processor, cause theprocessor to: assign a plurality of different phase values to aplurality of at least three different source transducers of theplurality of transducers; exciting the at least three source transducersin accordance with the assigned different phase values to generate aplurality of ultrasound waveforms within the tissue medium; receivingdata from a plurality of receiving transducers of the plurality oftransducers in accordance with transmissions and reflections of theplurality of ultrasound waveforms within the tissue medium; andcalculating a search direction based on data from the receivingtransducers, wherein the memory further stores instructions that, whenexecuted by the processor, cause the processor to perform a numericalsimulation of forward propagation of wavefields from the sourcetransducers and backward propagation of wavefields from the receivingtransducers, wherein the search direction is calculated based on theforward propagation of wavefields and the backward propagation ofwavefields, wherein the memory further stores instructions that, whenexecuted by the processor, cause the processor to: update a model basedon the search direction; and compute an ultrasound waveform tomographyimage reconstruction in accordance with the updated model, wherein thememory further stores instructions that, when executed by the processor,cause the processor to perform numerical waveform inversion to generatethe ultrasound waveform tomography image reconstruction, and wherein theplurality of different phase values are assigned during the numericalwaveform inversion.
 5. The ultrasound tomography imaging system of claim4, wherein the memory further stores instructions that, when executed bythe processor, cause the processor to: receive a transmission signal anda reflection signal at one of the receiving transducers within the oneor more ultrasound transducer arrays; and generate an ultrasoundwaveform tomography image reconstruction using the data received inaccordance with the transmission signal and the reflection signal.
 6. Anultrasound tomography imaging system for imaging a tissue mediumcomprising: two or more ultrasound transducer arrays spaced apart fromeach other, each of the ultrasound transducer arrays comprising aplurality of transducers; a processor; and memory storing instructionsthat, when executed by the processor, cause the processor to: assign aplurality of different phase values to a plurality of at least threedifferent source transducers of the plurality of transducers; excitingthe at least three source transducers in accordance with the assigneddifferent phase values to generate a plurality of ultrasound waveformswithin the tissue medium; receiving data from a plurality of receivingtransducers of the plurality of transducers in accordance withtransmissions and reflections of the plurality of ultrasound waveformswithin the tissue medium; and calculating a search direction based ondata from the receiving transducers, wherein the memory further storesinstructions that, when executed by the processor, cause the processorto perform a numerical simulation of forward propagation of wavefieldsfrom the source transducers and backward propagation of wavefields fromthe receiving transducers, wherein the search direction is calculatedbased on the forward propagation of wavefields and the backwardpropagation of wavefields, wherein the memory further storesinstructions that, when executed by the processor, cause the processorto: update a model based on the search direction; and compute anultrasound waveform tomography image reconstruction in accordance withthe updated model, and wherein the ultrasound wave tomography imagereconstruction is a function of:${{E(m)} = {\min\limits_{m}{\sum\limits_{s = 1}^{N_{s}}{\int{\lbrack {{d_{s}(t)} - {p_{S}( {m,t} )}} \rbrack^{2}dt}}}}},$where E(m) is a misfit function, d is one of transmission data andreflection data, p is a simulated waveform from the numericalsimulation, s is a source index indicating one of the sourcetransducers, N_(s) is the number of source transducers, and m is a modelparameter of the model.